Numerical experiments are performed using a recently published formalism [ Phys. Rev. A 88, 013419 (2013)] for computing the transient absorption of an attosecond x-ray probe by a molecule in a nonstationary valence-excited state. This study makes use of an all-electron correlated electronic-structure model to compute electronic dynamics ensuing after a localized excitation on a model chromophore group. Simulated absorption of a delayed attosecond pulse is then used to investigate the presence of an extra valence electron or vacancy around atoms of a given element as a function of time, by tuning the carrier frequency to the associated core-valence energy gap. We show correlations between the predicted absorption of such pulses and visualizations of the particle and hole locations in test molecules. Given the strong role played by the relative orientation of the molecules and the probe polarization, results are presented for a few different alignment schemes. For the molecules studied, effective pump-induced alignment is sufficient to recover easily interpreted information.

As experimental techniques begin to probe electronic motions in increasing detail, the need is arising for compact and informative visualisations of simulations of such processes. The inherent challenge is that a full many-electron wavefunction is a high-dimensional object, representing the complicated correlations of strongly repulsive bodies in a small molecular volume. A general procedure is needed to distill this to a smaller amount of information that does not rely on any specific level of approximation. The result should allow for easy and intuitive interpretation while drawing out nontrivial aspects of the underlying many-body dynamics, such as the complex phase information inherent of a nonstationary state. Current visualisation schemes based on physical observables or the qualitative information contained in simple wavefunctions, such as time-dependent configuration-interaction-singles (TD-CIS) and time-dependent self-consistent-field (TD-SCF), are discussed. This information is compared to an analysis based on the one-body reduced density operator (1-RDO), which is well-defined for general wavefunctions. It is seen that the distinction between two paradigms of many-body dynamics, electron transport and energy transport, is reflected in the coherences of a difference-1-RDO, or lack thereof.

A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and permanently folded into an effective Hamiltonian, thus avoiding redundant evaluations of local relaxations associated with coupled fluctuations. A companion article shows that a low-scaling step may be used to cast the electronic Hamiltonians of real systems into the form required. Two proof-of-principle demonstrations are presented here for non-covalent interactions. One uses harmonic oscillators, for which accuracy and algorithm structure can be carefully controlled in comparisons. The other uses small electronic systems (Be atoms) to demonstrate compelling accuracy and efficiency, also when inter-fragment electron exchange and charge transfer must be handled. Since the cost of the global calculation does not depend directly on the correlation models used for the fragments, this should provide a way to incorporate difficult electronic structure problems into large systems. This framework opens a promising path for building tunable, systematically improvable methods to capture properties of systems interacting with a large number of other systems. The extension to excited states is also straightforward.

We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment electron exchange and charge transfer. Familiar electronic structure approaches can be applied to the renormalised Hamiltonian. For efficiency, the basis for each fragment can be truncated, removing high-energy local arrangements of electrons from consideration, and effectively defining collective coordinates for the fragments. For a large number of problems (especially for non-covalently interacting fragments), this has the potential to fold the majority of electron correlation into the effective Hamiltonian, and it should provide a robust approach to incorporating difficult electronic structure problems into large systems. The number of terms in the exactly transformed Hamiltonian formally scales quartically with system size, but this can be reduced to quadratic in the mesoscopic regime, to within an arbitrary error tolerance. Finally, all but a linear-scaling number of these terms may be efficiently decomposed in terms of electrostatic interactions between a linear-scaling number of pre-computed transition densities. In a companion article, this formalism is applied to an excitonic variant of coupled-cluster theory.

This work introduces the Coupled-Resonances (CR) line shape as a theoretically robust model for analyzing asymmetric peaks in photoelectron spectra, broadly applicable across various materials. The CR line shape extends the conventional Lorentzian distribution by incorporating an interference term that contributes to the peak asymmetry. This new approach addresses limitations of the widely used Doniach- Šunjić (D&S) model, which is often applied beyond its intended scope of metals with high densities of states at the Fermi level due to a lack of viable alternatives. Unlike the DS line shape, the CR model is integrable, enabling its use in precise chemical composition calculations, and it consistently provides superior fits to experimental data. The CR model’s versatility is evident in its ability to simplify to a Lorentzian for a single resonance. However, with multiple resonance states, the total line shape is no longer a simple summation of individual peak contributions. Instead, a significant interference term emerges, profoundly contributing to the observed peak asymmetry and shifting the maximum peak intensity. This highlights the critical need to consider interference terms in multiplet calculations of lineshapes. The CR line shape has been implemented in the freely available software, AAnalyzer. While most asymmetric peaks are accurately described by CR Type-II (two resonances), some require CR Type-III (three resonances) for optimal fitting, as demonstrated in the included examples. Ultimately, the CR model offers a more accurate and versatile approach to analyzing asymmetric lineshapes in photoemission spectroscopy, with broad applicability to a wide range of materials, including metals.

The background signal in X-ray Photoelectron Spectroscopy (XPS) consists of extrinsic and intrinsic components. This study focuses on characterizing the intrinsic background, particularly its structure across an extended binding energy (BE) range beyond the vicinity of the main photoelectron peak. The structure of the intrinsic background in the extended region can be reproduced through a rich set of wide Gaussian peaks. In the near-peak region, the intrinsic background is successfully characterized using the empirical Shirley algorithm. Since the Shirley algorithm fails when applied to extended energy regions by overshooting the experimental signal, a modified version must be employed that decays beyond the near-peak region. We found that a functional form flat near the peak (as in the Shirley algorithm) decays in a Gaussian-like manner for higher binding energies, satisfactorily reproduces the experimental data, and allows for revealing the rest of the rich structure of the intrinsic background. For this reason, we termed it a narrow-Shirley (NS) background. The characterization of the structure of the extended region of the intrinsic background enables the qualitative exploration of its physical origin. Building on previous work linking the near-peak Shirley signal to Interchannel Coupling with Valence Band Losses (ICVBL), we propose and provide qualitative evidence that this ICVBL mechanism is responsible for the entire intrinsic background structure across the extended energy range; this mechanism involves the absorption of a photon by a participating core level. Two of the predictions of the ICVBL mechanism are tested by comparing the structure of the intrinsic background with Auger Electron Spectroscopy (AES) and X-ray Absorption Spectroscopy (XAS) data; a third prediction, the expected modulation of the intrinsic background with photon energies around the threshold of the participating core level, is tested through synchrotron experiments.